{"id":34861,"date":"2020-02-03T00:23:06","date_gmt":"2020-02-02T16:23:06","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=34861"},"modified":"2020-03-02T10:03:08","modified_gmt":"2020-03-02T02:03:08","slug":"%e5%be%ae%e7%a9%8d%e5%88%86%e7%9a%84dx%e4%ba%8c%ef%bc%9a%e5%be%9e%e7%b4%9a%e6%95%b8%e5%88%b0%e5%87%bd%e6%95%b8%e8%ab%96","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=34861","title":{"rendered":"\u5fae\u7a4d\u5206\u7684dx(\u4e8c)\uff1a\u5f9e\u7d1a\u6578\u5230\u51fd\u6578\u8ad6"},"content":{"rendered":"<p><span style=\"color: #333399;\"><strong>\u4e0a\u56de\u6211\u5011\u7c21\u55ae\u4ecb\u7d39\u4e86\u300c\u7121\u9650\u5c0f\u300d\u7684\u6982\u5ff5\uff0c\u800c\u9019\u56de\u6211\u5011\u5c07\u6642\u5149\u5012\u6d41\uff0c\u770b\u770b\u5728\u5fae\u7a4d\u5206\u525b\u525b\u767c\u660e\u5f8c\u7684\u5927\u7d04100\u5e74\u671f\u9593\u7684\u6a23\u8c8c\uff0c\u4ee5\u53ca\u9019100\u5e74\u4e4b\u5f8c\u50ac\u751f\u51fa\u7684\u300c\u6975\u9650\u300d\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u65bc\u6b64\u540c\u6642\uff0c\u8cea\u7591\u300c\u51fd\u6578\u300d\u7684\u601d\u6f6e\u3002<\/strong><\/span><\/p>\n<p><strong>\u64b0\u6587\uff5c<\/strong><strong>\u674e\u9f8d\u6b23<\/strong><\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u5341\u4e03\u3001\u5341\u516b\u4e16\u7d00\u7684\u5fae\u7a4d\u5206<\/strong><\/span><\/p>\n<p>17\u4e16\u7d00\u4e2d\u671f\u5fae\u7a4d\u5206\u767c\u660e\u4e4b\u5f8c\uff0c\u6709\u8a31\u591a\u672a\u89e3\u7684\u554f\u984c\u5f97\u5230\u91cd\u5927\u7a81\u7834\u3002\u4f8b\u5982\u5728\u5e7e\u4f55\u65b9\u9762\uff0c\u672c\u4f86\u53ea\u80fd\u8655\u7406\u4e8c\u6b21\u66f2\u7dda\u7684\u554f\u984c\uff0c\u4f46\u5fae\u7a4d\u5206\u7528\u5728\u5176\u4ed6\u66f2\u7dda\u4e5f\u6709\u7528\u3002\u5728\u8655\u7406\u904e\u9019\u4e9b\u554f\u984c\u5f8c\uff0c\u6709\u5f88\u591a\u66f2\u7dda\u90fd\u53ef\u4ee5\u5beb\u6210\u5e42\u7d1a\u6578 (power series)\u2500\u2500\u7c21\u55ae\u4f86\u8aaa\u5c31\u662f\u628a\u591a\u9805\u5f0f\u8b8a\u6210\u7121\u9650\u591a\u9805\u3002\u4f8b\u5982\uff1a<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-34877 alignnone\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/1.png\" alt=\"\" width=\"356\" height=\"55\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/1.png 356w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/1-300x46.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-34878\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/2.png\" alt=\"\" width=\"359\" height=\"55\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/2.png 359w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/2-300x46.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>\u725b\u9813\u5728\u5206\u985e\u4e09\u6b21\u66f2\u7dda\u6642\u5c1a\u9808\u501f\u52a9\u5fae\u7a4d\u5206\uff0c\u5fae\u7a4d\u5206\u53c8\u80fd\u8655\u7406\u7121\u9650\u591a\u9805\u7684\u591a\u9805\u5f0f\uff0c\u591a\u9ebc\u632f\u596e\u4eba\u5fc3\u554a\uff01\u4e5f\u96e3\u602a \u5e03\u9b6f\u514b\u00b7\u6cf0\u52d2(Brook Taylor\uff0c1685\u25001731) \u6703\u60f3\u8981\u628a\u6240\u6709\u51fd\u6578\u90fd\u8b8a\u6210\u5e42\u7d1a\u6578\uff0c\u800c\u9019\u500b\u5e42\u7d1a\u6578\u7a31\u70ba\u6cf0\u52d2\u5c55\u958b\u5f0f (Taylor expansion)\uff1a<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-34879 aligncenter\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/3.png\" alt=\"\" width=\"701\" height=\"52\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/3.png 701w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/3-300x22.png 300w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/p>\n<p>\u9806\u5e36\u4e00\u63d0\uff0c\u5217\u7fc1\u54c8\u7279\u00b7\u6b50\u62c9(Leonhard Euler\uff0c1707\u25001783) \u5c0d\u65bc\u7121\u9650\u591a\u500b\u6578\u76f8\u52a0\u9019\u4ef6\u4e8b\u6709\u7368\u5230\u7684\u898b\u89e3\u3002\u5e42\u7d1a\u6578\u5728\u4ed6\u624b\u4e2d\u80fd\u6709\u5343\u8b8a\u842c\u5316\uff0c\u751a\u81f3\u80fd\u5920\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n<p>\u53ef\u662f\u5e42\u7d1a\u6578\u4e26\u6c92\u6709\u90a3\u9ebc\u7f8e\u597d\u3002\u4f8b\u5982\u6211\u5011\u77e5\u9053\u7b49\u6bd4\u7d1a\u6578\u7684\u516c\u5f0f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-34881 aligncenter\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/4.png\" alt=\"\" width=\"219\" height=\"48\"><\/p>\n<p>\u6b50\u62c9\u6ce8\u610f\u5230\u4ee5\u4e0b\u7684\u63a8\u8ad6 (\u5206\u5225\u4ee3\u5165 r=n \u548c r=1\/n) \u4e0d\u5408\u7406\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34882\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/5.png\" alt=\"\" width=\"782\" height=\"121\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/5.png 782w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/5-300x46.png 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/5-768x119.png 768w\" sizes=\"(max-width: 782px) 100vw, 782px\" \/><\/p>\n<p>\u6842\u6597\u00b7\u683c\u7136\u8fea(Guido Grandi\uff0c1671\u25001742) \u4e5f\u6ce8\u610f\u5230\u5728\u7b49\u6bd4\u7d1a\u6578\u4e2d\u4ee3\u5165 r=-1 \u7684\u8a71\u6703\u5f97\u5230<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34883\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/6.png\" alt=\"\" width=\"679\" height=\"53\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/6.png 679w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/6-300x23.png 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><\/p>\n<p>\u9019\u5e7e\u500b\u4f8b\u5b50\u90fd\u986f\u793a\u51fa\u6211\u5011\u8981\u66f4\u56b4\u8085\u5730\u770b\u5f85\u51fd\u6578\u7684\u904b\u7b97\u3002<\/p>\n<p><strong>&nbsp;<\/strong><\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u6975\u9650 (limit)<\/strong><\/span><\/p>\n<p>\u6211\u5011\u5c0d\u65bc\u6709\u9650\u5c0f\u7684\u6578\u505a\u70ba\u5206\u6bcd\u3001\u6709\u9650\u591a\u500b\u6578\u76f8\u52a0\u90fd\u6c92\u6709\u554f\u984c\uff0c\u53ef\u662f\u7121\u9650\u5c0f\u7684\u6578\u505a\u70ba\u5206\u6bcd\u3001\u7121\u9650\u591a\u500b\u6578\u76f8\u52a0\u672c\u4f86\u5c31\u5927\u6709\u554f\u984c\u3002\u6642\u9593\u56de\u523018\u4e16\u7d00\u7684\u82f1\u570b\uff0c\u8a79\u59c6\u58eb\u00b7\u6731\u6797(James Jurin\uff0c1684\u25001750) \u548c \u73ed\u54f2\u660e\u00b7\u7f85\u8cd3\u65af(Benjamin Robins\uff0c1707\u25001751) \u70ba\u9996\u7684\u5169\u6d3e\u5b78\u8005\u57fa\u65bc\u725b\u9813\u6240\u63d0\u51fa\u7684\u300c\u6975\u9650\u300d(limit) \u7684\u96db\u5f62\u5c55\u958b\u7b46\u6230\uff0c\u6216\u8a31\u6709\u5f71\u97ff\u5230\u5f8c\u4eba\u3002\u6b50\u9678\u65b9\u9762\uff0c\u5189\u52d2\u5b8f\u00b7\u9054\u6717\u8c9d\u723e(Jean-le-Rond d'Alembert\uff0c1717\u25001783) \u904b\u7528\u300c\u6975\u9650\u300d\u91cd\u65b0\u8a6e\u91cb\u5fae\u5206\u3002\u8b6c\u5982\u66f2\u7dda y=f(x) \u4e0a\u6709\u5169\u500b\u9ede (x,f(x)) \u548c (x+\u0394x,f(x+\u0394x))\uff0c\u5c07\u5169\u9ede\u9023\u8d77\u4f86\u5f97\u5230\u7684\u76f4\u7dda\u7a31\u70ba\u5272\u7dda (secant line)\u3002\u7576 \u0394x \u8d8a\u5c0f\uff0c\u9019\u689d\u76f4\u7dda\u5c31\u8d8a\u63a5\u8fd1 (x,f(x)) \u7684\u5207\u7dda (tangent line)\uff0c\u800c\u5272\u7dda\u7684\u659c\u7387\u4e5f\u5f80\u5207\u7dda\u7684\u659c\u7387\u9760\u8fd1\uff0c\u800c\u5207\u7dda\u7684\u659c\u7387\u5c31\u662f\u5fae\u5206\u3002<\/p>\n<figure id=\"attachment_34868\" aria-describedby=\"caption-attachment-34868\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-34868\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/7.png\" alt=\"\" width=\"500\" height=\"448\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/7.png 668w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/7-300x269.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-34868\" class=\"wp-caption-text\">\u57161\uff1a\u5272\u7dda\u8207\u5207\u7dda\u3002\u5716\u7247\u4f86\u6e90\uff1a\u300aIntroduction to Calculus and Analysis\u300b\u3002R. Courant\u3001F. John \u8457\u3002\u521d\u7248(1989)\u3002Springer-Verlag \u51fa\u7248(\u7d10\u7d04\/\u67cf\u6797\/\u6d77\u5fb7\u5821)<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>\u5f9e\u6709\u9650\u5c0f\u7684 \u0394x \u6a21\u64ec\u7121\u9650\u5c0f\u7684 dx\uff0c\u9019\u5c31\u662f\u300c\u6975\u9650\u300d\u3002\u5f9e\u7b97\u5f0f\u4e2d\u53ef\u4ee5\u770b\u51fa\u5176\u5c0d\u61c9\u95dc\u4fc2\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34884\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/8.png\" alt=\"\" width=\"133\" height=\"54\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/8.png 133w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/8-130x54.png 130w\" sizes=\"(max-width: 133px) 100vw, 133px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u4f86\u5230\u4e8619\u4e16\u7d00\uff0c\u5967\u53e4\u65af\u4e01\u00b7\u67ef\u897f(Augustin Cauchy\uff0c1789\u25001857) \u9032\u4e00\u6b65\u8a6e\u91cb\uff0c\u70ba\u4e86\u65b9\u4fbf\u61c9\u7528\u5230\u8b49\u660e\u4e2d\uff0c\u5728\u6558\u8ff0\u6642\u9700\u8981\u5148\u5047\u8a2d\u6211\u5011\u77e5\u9053\u5272\u7dda\u7684\u659c\u7387\u9760\u8fd1\u7684\u662f\u54ea\u500b\u6578\uff0c\u518d\u628a\u9019\u500b\u6578\u7a31\u70ba\u5272\u7dda\u659c\u7387\u7684\u6975\u9650\u3002\u9054\u6717\u8c9d\u723e\u3001\u67ef\u897f\u7528\u6587\u5b57\u63cf\u8ff0\u6975\u9650\u800c\u6709\u9ede\u62d7\u53e3\uff0c\u5f8c\u4f86 \u5361\u723e\u00b7\u5916\u723e\u8a31\u7279\u62c9\u65af(Karl Weierstra\u00df\uff0c1815\u25001897) \u767c\u660e\u7684\u300c\u03b5-\u03b4\u8a9e\u8a00\u300d\u6558\u8ff0\u8d77\u4f86\u66f4\u7cbe\u7c21\u4f46\u7cbe\u795e\u76f8\u540c\u3002<\/p>\n<p>\u81f3\u65bc\u7a4d\u5206\u65b9\u9762\uff0c\u56de\u5230\u539f\u672c\u7684\u65b9\u6cd5\uff0c\u7528\u9577\u65b9\u5f62\u9762\u7a4d\u4f86\u4f30\u8a08\u5716\u5f62\u7684\u9762\u7a4d\u3002\u9577\u65b9\u5f62\u7684\u5bec\u5ea6\u70ba \u0394x<sup>\u8a3b1<\/sup>\uff0c\u9ad8\u5ea6\u548c\u6bcf\u4e00\u5c0f\u6bb5\u66f2\u7dda\u7684\u5de6\u7aef\u4e00\u6a23\u9ad8\uff0c\u5982\u4e0b\u5716\u6240\u793a\uff1a<\/p>\n<figure id=\"attachment_34870\" aria-describedby=\"caption-attachment-34870\" style=\"width: 689px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-34870 size-full\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/9.png\" alt=\"\" width=\"689\" height=\"481\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/9.png 689w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/9-300x209.png 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/9-130x90.png 130w\" sizes=\"(max-width: 689px) 100vw, 689px\" \/><figcaption id=\"caption-attachment-34870\" class=\"wp-caption-text\">\u57162\uff1a\u9ece\u66fc\u548c\u3002<br \/>\u5716\u7247\u4f86\u6e90\uff1a\u300aElementary Calculus: An Infinitesimal Approach\u300b\u3002H. Keisler \u8457\u30022019\u5e749\u6708\u4fee\u8a02\u7248\u3002\u65bc\u7db2\u8def\u514d\u8cbb\u516c\u958b\u3002\u7db2\u5740\uff1ahttp:\/\/www.math.wisc.edu\/~keisler\/calc.html\u3002\u53e6\u6709\u5370\u5237\u7248\uff1a\u7b2c\u4e09\u7248(2012)\u3002Dover \u51fa\u7248(\u7d10\u7d04)\u3002<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p>\u7576 \u0394x \u6709\u9650\u5c0f\u3001\u9577\u65b9\u5f62\u6709\u9650\u591a\u6642\u7684\u9762\u7a4d\u548c\u7a31\u70ba\u9ece\u66fc\u548c (Riemann sum)\u3002\u7576\u5207\u5272\u8d8a\u4f86\u8d8a\u7d30\u6642\uff0c\u9ece\u66fc\u548c\u7684\u6975\u9650\u5c31\u662f\u66f2\u7dda\u4e0b\u7684\u9762\u7a4d\u3002\u53ef\u4ee5\u7528\u7b97\u5f0f\u8868\u9054\u70ba\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34885\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/10.png\" alt=\"\" width=\"271\" height=\"56\"><\/p>\n<p>\u540c\u6a23\u662f\u7528\u6709\u9650\u5c0f\u7684 \u0394x \u6a21\u64ec\u7121\u9650\u5c0f\u7684 dx\u3002<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cf\u51fd\u6578\u8ad6 (theory of functions)<\/strong><\/span><\/p>\n<p>\u51fd\u6578\u7684\u610f\u7fa9\u5f9e18\u4e16\u7d00\u523019\u4e16\u7d00\u7d93\u6b77\u4e00\u5927\u8f49\u8b8a\u3002\u539f\u672c\u7684\u51fd\u6578\u6240\u8c61\u5fb5\u7684\u662f\u300c\u8a08\u7b97\u65b9\u6cd5\u300d\uff0c\u5fc5\u9700\u8981\u662f\u300c\u53ef\u4ee5\u7b97\u7684\u300d\u3002\u5f8c\u4f86\u767c\u73fe\u51fd\u6578\u80fd\u5426\u8a08\u7b97\u3001\u751a\u81f3\u662f\u80fd\u5426\u63cf\u8ff0\u51fa\u4f86\uff0c\u4f3c\u4e4e\u8ddf\u80fd\u5426\u505a\u5fae\u7a4d\u5206\u6c92\u4ec0\u9ebc\u95dc\u4fc2\u4e86\u3002\u56e0\u800c\u9700\u8981\u91dd\u5c0d\u80fd\u5426\u505a\u5fae\u7a4d\u5206\u7684\u90e8\u5206\u91cd\u65b0\u5be9\u8996\u3002\u4f8b\u5982\u4e0b\u5217\u5169\u500b\u554f\u984c\uff1a<\/p>\n<p><strong>\u4e00\u3001\u7121\u7aae\u548c\u662f\u5426\u771f\u7684\u662f\u6578\uff1f\u54ea\u4e9b\u51fd\u6578\u662f\u5e42\u7d1a\u6578\uff1f<\/strong><\/p>\n<p>\u70ba\u4f55\u8981\u554f\u9019\u500b\u554f\u984c\uff1f\u56e0\u70ba\u67ef\u897f\u767c\u73fe\u4e00\u500b\u6cf0\u52d2\u5c55\u958b\u5f0f\u70ba 0 \u4f46\u539f\u51fd\u6578\u4e0d\u662f 0 \u7684\u51fd\u6578\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34886\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/11.png\" alt=\"\" width=\"230\" height=\"83\"><\/p>\n<p>\u6240\u4ee5\u9019\u500b\u51fd\u6578\u4e0d\u662f\u4e00\u500b\u5e42\u7d1a\u6578\u3002<\/p>\n<p>\u4ee5\u4e00\u500b\u5e42\u7d1a\u6578<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-34887\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/12.png\" alt=\"\" width=\"470\" height=\"37\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/12.png 470w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2019\/02\/12-300x24.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>\u4f86\u8aaa\uff0c\u7576 |x-a| \u8d8a\u5c0f<sup>\u8a3b2<\/sup>\uff0c\u8d8a\u6709\u6a5f\u6703\u8b93\u7e3d\u548c\u6709\u9650\uff0c\u800c\u67ef\u897f\u4e5f\u8b49\u660e\u4e86\u78ba\u5be6\u5982\u6b64\u3002\u7528\u67ef\u897f\u7684\u6839\u503c\u6aa2\u9a57\u6cd5 (root test)\uff0c\u53ef\u4ee5\u627e\u5230\u6536\u6582\u534a\u5f91 (radius of convergence)\u3002\u5728 |x-a| \u5c0f\u65bc\u6536\u6582\u534a\u5f91\u6642\u90fd\u80fd\u7576\u505a\u51fd\u6578\u4e26\u4e14\u752818\u4e16\u7d00\u7684\u65b9\u6cd5\u505a\u5fae\u7a4d\u5206\u3002\u53cd\u4e4b\uff0c\u5728 |x-a| \u7b49\u65bc\u6536\u6582\u534a\u5f91\u6642\u4e00\u5b9a\u6703\u5728\u67d0\u4e9b\u9ede\u9047\u5230\u7e3d\u548c\u70ba\u7121\u9650\u5927\u7684\u554f\u984c\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u4e8c\u3001\u4ec0\u9ebc\u51fd\u6578\u53ef\u4ee5\u7a4d\u5206\uff1f<\/strong><\/p>\n<p>\u67ef\u897f\u9996\u5148\u7528\u6975\u9650\u63cf\u8ff0\u7a4d\u5206\u4e4b\u5f8c\uff0c\u8c9d\u6069\u54c8\u7279\u00b7\u9ece\u66fc(Bernhard Riemann\uff0c1826\u25001866) \u8a8d\u70ba\u4e26\u6c92\u6709\u7406\u7531\u8981\u7528\u5de6\u7aef\u9ede\uff0c\u800c\u6539\u6210\u7528\u66f2\u7dda\u4e0a\u4efb\u4e00\u9ede\uff0c\u4e26\u4e14\u53ea\u6709\u7576\u4efb\u610f\u53d6\u6cd5\u90fd\u5f97\u5230\u540c\u4e00\u500b\u6975\u9650\u6642\u624d\u7b97\u662f\u53ef\u4ee5\u7a4d\u5206\u3002\u63a5\u4e0b\u4f86\u53c8\u9032\u4e00\u6b65\u8a66\u5716\u6539\u9032\u7684\u6709\u5f88\u591a\uff0c\u4e3b\u8981\u6709\uff1a\u6602\u91cc\u00b7\u52d2\u8c9d\u683c(Henri Lebesgue\uff0c1875\u25001941)\u3001\u6258\u99ac\u65af\u00b7\u65af\u63d0\u723e\u5207\u65af(Thomas Stieltjes\uff0c1856\u25001894)\u3001\u7d04\u7ff0\u00b7\u62c9\u8463(Johann Radon\uff0c1887\u25001956)\u3002\u5404\u500b\u7406\u8ad6\u7684\u300c\u80fd\u5920\u7a4d\u5206\u300d\u7684\u51fd\u6578\u5404\u81ea\u7565\u6709\u4e0d\u540c\u3002<\/p>\n<p>\u800c\u9019\u5169\u500b\u554f\u984c\u4e5f\u5206\u5225\u6210\u70ba\u8907\u8b8a\u5206\u6790 (complex analysis)\u3001\u5be6\u8b8a\u5206\u6790 (real analysis) \u7684\u958b\u7aef\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u8a3b\u89e3\uff1a<br \/>\n<\/strong>[1] \u5728\u67ef\u897f\u548c\u9ece\u66fc\u7684\u5b9a\u7fa9\u4e2d\uff0c\u9577\u65b9\u5f62\u7684\u5bec\u5ea6\u4e0d\u5fc5\u76f8\u7b49\uff0c\u4f46\u662f\u5fc5\u9808\u5728\u53d6\u6975\u9650\u6642\u5168\u90e8\u7e2e\u5c0f\u81f3 0\u3002<br \/>\n[2] \u5169\u76f4\u5283\u7684\u8a18\u865f\u70ba\u8907\u6578\u7684\u7d55\u5c0d\u503c\u3002<\/p>\n<p><strong>\u53c3\u8003\u8cc7\u6599<br \/>\n<\/strong>[1] \u300aA History of Mathematics\u300b\u3002F. Cajori \u8457\u3002\u7b2c\u4e8c\u7248(1961)\u3002Macmillan \u51fa\u7248(\u7d10\u7d04)\u3002<br \/>\n[2] \u300aA History of Mathematics\u300b\u3002U. Merzbach\u3001C. Boyer \u8457\u3002\u7b2c\u4e09\u7248(2011)\u3002Wiley \u51fa\u7248(\u7d10\u6fa4\u897f)\u3002<br \/>\n[3] \u300aThe Calculus Gallery: Masterpieces from Newton to Lebesgue\u300b\u3002W. Dunham \u8457\u3002\u521d\u7248(2005)\u3002Princeton University Press \u51fa\u7248(\u7d10\u6fa4\u897f)\u3002<br \/>\n[4] \u3008Newton and Infinite Series\u3009\u3002\u5927\u82f1\u767e\u79d1\u5168\u66f8\u3002\u65bc\u7db2\u8def\u516c\u958b\u3002\u7db2\u5740\uff1a<a href=\"https:\/\/www.britannica.com\/topic\/Newton-and-Infinite-Series-1368282\">https:\/\/www.britannica.com\/topic\/Newton-and-Infinite-Series-1368282<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e0a\u56de\u6211\u5011\u7c21\u55ae\u4ecb\u7d39\u4e86\u300c\u7121\u9650\u5c0f\u300d\u7684\u6982\u5ff5\uff0c\u800c\u9019\u56de\u6211\u5011\u5c07\u6642\u5149\u5012\u6d41\uff0c\u770b\u770b\u5728\u5fae\u7a4d\u5206\u525b\u525b\u767c\u660e\u5f8c\u7684\u5927\u7d04100\u5e74\u671f\u9593\u7684\u6a23\u8c8c\uff0c\u4ee5\u53ca\u9019100\u5e74\u4e4b\u5f8c\u50ac\u751f\u51fa\u7684\u300c\u6975\u9650\u300d\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u65bc\u6b64\u540c\u6642\uff0c\u8cea\u7591\u300c\u51fd\u6578\u300d\u7684\u601d\u6f6e\u3002<\/p>\n","protected":false},"author":20,"featured_media":34874,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,148,2977],"tags":[4479,4516,1229,4515,4514],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2020\/01\/\u5c01\u9762.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34861"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=34861"}],"version-history":[{"count":6,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34861\/revisions"}],"predecessor-version":[{"id":34890,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/34861\/revisions\/34890"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/34874"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=34861"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=34861"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=34861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}